Modeling sign concordance of quantile regression residuals with multiple outcomes

Columbu Silvia (), Frumento Paolo and Bottai Matteo
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Columbu Silvia: University of Cagliari, Cagliari, Italy
Frumento Paolo: University of Pisa, Pisa, Italy
Bottai Matteo: Karolinska Institute, Solna, Stockholm, Sweden

The International Journal of Biostatistics, 2023, vol. 19, issue 1, 97-110

Abstract: Quantile regression permits describing how quantiles of a scalar response variable depend on a set of predictors. Because a unique definition of multivariate quantiles is lacking, extending quantile regression to multivariate responses is somewhat complicated. In this paper, we describe a simple approach based on a two-step procedure: in the first step, quantile regression is applied to each response separately; in the second step, the joint distribution of the signs of the residuals is modeled through multinomial regression. The described approach does not require a multidimensional definition of quantiles, and can be used to capture important features of a multivariate response and assess the effects of covariates on the correlation structure. We apply the proposed method to analyze two different datasets.

Keywords: conditional correlation; multinomial model; multiple quantiles; multivariate regression; sign-concordance (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/ijb-2022-0020

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